OFFSET

2,1

COMMENTS

All n > 1 such that (# of 1's) != (# of 0's) in the base 2 expansion of floor(n/2). The numerators of the series are A126389.

LINKS

Jonathan Sondow, Double integrals for Euler's constant and ln(4/Pi) and an analog of Hadjicostas's formula, arXiv:math/0211148 [math.CA], 2002-2004.

Jonathan Sondow, Double integrals for Euler's constant and ln(4/Pi) and an analog of Hadjicostas's formula, Amer. Math. Monthly 112 (2005), 61-65.

Jonathan Sondow, New Vacca-Type Rational Series for Euler's Constant and Its "Alternating" Analog ln(4/Pi), arXiv:math/0508042 [math.NT], 2005.

Jonathan Sondow, New Vacca-Type Rational Series for Euler's Constant and Its "Alternating" Analog ln(4/Pi), Additive Number Theory, Festschrift In Honor of the Sixtieth Birthday of Melvyn B. Nathanson (D. Chudnovsky and G. Chudnovsky, eds.), Springer, 2010, pp. 331-340.

Eric Weisstein's MathWorld, Digit Count.

FORMULA

log(4/Pi) = 1/2 - 1/3 + 2/6 - 2/7 - 1/8 + 1/9 + 1/10 - 1/11 + 1/12 - 1/13 + 3/14 - 3/15 - 2/16 + 2/17 + 2/22 - ...

EXAMPLE

floor(13/2) = 6 = 110 base 2, which has (# of 1's) = 2 != 1 = (#

of 0's), so 13 is a member.

MATHEMATICA

b[n_] := DigitCount[n, 2, 1] - DigitCount[n, 2, 0]; L = {}; Do[If[b[Floor[n/2]] != 0, L = Append[L, n]], {n, 2, 100}]; L

CROSSREFS

KEYWORD

base,nonn

AUTHOR

Jonathan Sondow, Jan 01 2007

STATUS

approved